Some Results on Secant Varieties Leading to a Geometric Flip Construction

@article{Vermeire1999SomeRO,
  title={Some Results on Secant Varieties Leading to a Geometric Flip Construction},
  author={Peter Vermeire},
  journal={Compositio Mathematica},
  year={1999},
  volume={125},
  pages={263-282}
}
We study the relationship between the equations defining a projective variety and properties of its secant varieties. In particular, we use information about the syzygies among the defining equations to derive smoothness and normality statements about SecX and also to obtain information about linear systems on the blow up of projective space along a variety X. We use these results to geometrically construct, for varieties of arbitrary dimension, a flip first described in the case of curves by M… CONTINUE READING

References

Publications referenced by this paper.
SHOWING 1-10 OF 19 REFERENCES

A Wísniewski, A View on Contractions of Higher-Dimensional Varieties, in Algebraic Geometry

J M Andreatta
  • Santa Cruz
  • 1995

Lazarsfeld, Syzygies and Koszul Cohomology of Smooth Projective Varieties of Arbitrary Dimension

R L Ein
  • Invent. Math
  • 1993

Complete extensions and their map to moduli space, in Complex Projective Geometry

A Bertram
  • London Math. Soc. Lecture Note Series
  • 1992